Cool MCMC papers

Dec.
25th
2014

I’ve been reading a lot about Bayesian inference and MCMC lately. Not about the generalities, which I have been using for years, but rather about the technicalities of advanced algorithms. I recently realised that the tools that we cosmologists use are very basic, and sometimes far from the actual state of the art in statistical inference. Another reason is that I have started a couple of projects that require more advanced tools and tricks to become tractable. Anyway, here is a few papers that I found clear and detailed, while intelligible by physicists I think. I will update this post as I read more.

Hamiltonian Monte Carlo (HMC)

HMC is a powerful MCMC method to explore complicated distributions with high acceptance rates and a lot of technical and computational flexibility.

MCMC using Hamiltonian dynamics by Radford M. Neal. A very progressive and pedagogic introduction to HMC techniques, their variants and latest developments. I particularly liked the clear presentation of the pros and cons of HMC illustrated on simple examples. Bonus point: it is a goldmine of references.

Sequential Monte Carlo (SMC) and Particle Filtering

SMC is a useful category of iterative algorithms for MCMC and optimisation, especially for Gaussian state space models and Bayesian networks.